Abstract:
Star and galaxy formation are fundamental to our understanding of the Universe. Despite decades of efforts by both observers and theorists there is no comprehensive theory for either due to the complexity of the physical processes involved (e.g., turbulence, gravity, radiation, magnetic fields). This makes numerical simulations the key tool for understanding how exactly these processes interact and what effect they have on the evolution of the Universe. However, simulations face significant challenges due to the extreme dynamic range and deep time hierarchy of the problem, making a simulation extremely costly even on the largest supercomputers. In this talk I will review some of the numerical methods used by state-of-the-art star and galaxy formation simulations (STARFORGE & FIRE) to tackle these challenges.
Bio:
I am a theoretical and computational astrophysicist. I am mostly interested in the rich phenomena of star formation. I utilize both analytical and numerical tools to answer questions like:
What regulates star formation?
What sets the characteristic mass of stars?
Why are stars clustered?
What determines the properties of stellar binaries?
How is star formation different in other galaxies?
These questions have far reaching implications beyond the field of star formation. The interpretation of observed starlight from any extragalactic sources rely on our understanding and assumptions about star formation. Similarily answering these questions would greatly enhance our knowledge about the circumstances of planet formation.
I am originally from Hungary where I got my bachelor's and master's degrees in physics. I received my PhD in phyiscs from the California Institute of Technology and I am currently a Cottrell postdoctoral fellow at the University of Texas at Austin.
Summary:
Software:
Challenges:
Compressible turbulence
Extreme dynamic range: individual stars to whole universe is 20 orders of magnitude
Feedback from small scales
Wind/radiation bubbles, shock waves: .1-1 light years
Protostellar outflows (gas jets blow out when stars form)
Supernovae have a large effect radius (can affect galaxy clusters)
Deep time hierarchy
Galaxy ~ 200Myr
Molecular cloud ~ 1Myr
Binary stars ~1 yr
Multi-species fluid
Hydrogen + Helium
Chemistry from different elements; small by mass but big effect on thermodynamics
Dust, formed by heavy elements; attenuates radiation
Tracking chemical species significantly increases memory use
Numerical approach
Conservative hydro method
Adaptive spatial scaling
Advanced adaptive timestepping
Sub-grid prescriptions
Smoothed Particle Hydrodynamics (SPH)
Lagrangian method: particles tracked individually as they flow over the grid
Particle positions smoothed using Gaussian kernel
Challenges: numerically unstable but manageable using artificial viscosity terms
Adaptive Mesh Refinement (AMR)
Eulerian fluid elements
Mesh elements have different sizes
Grid is structured (good mapping to compute hardware) but hierarchical to capture different scales
Can incorporate Lagrangian elements to deal with very dense regions of space
Key challenges:
Is that the grid is fixed in space, which has high errors for fast-moving flows
Shape of geometry imprints itself on the pattern of errors in the result
Quasi-Lagrangian Godunov methods (MF*)
Mesh moves with the flow
No preferred mesh geometry
Volume re-meshed periodically
Appropriate for complex flows
Rotating disk of many particles: star system, galaxy
Turbulent flows: Kelvin-Helmholtz, Rayleigh-Taylor instabilities
Their implementation
Good weak scaling upto 10^10 elements / 10^5 CPUs
Strong calling: > 3e10^4 cell/core
FIRE: > 7E10^4 cell/core
Star formation process
Gravity pulls gas in, stars form, blow out remaining gas
Hard to model because gravity is a long-range force
Need to “soften” gravity to reduce need for very small time steps
Use a Tree-Particle-Mesh method
Tree of meshes
Short-range forces done within mesh
Long-range forces done at various levels of precision across sub-trees of meshes
Gravity + Magnetohydrodynamics violates some conservations in MF* methods, so special schemes develop to solve this
Time-stepping
Different time scales
Don’t want to force all processes to use same tiny time step size
Time step must reflect the speed of causality in system (fast flows: tiny time steps)
Mesh moves with the flow, so acceleration also affects time step size
Need to focus on relative acceleration of different sub-elements (e.g. focus on Earth-moon relative acceleration separately from how sun accelerates them)
Sink particles
When we see a gas cell converging into a single place, replace with a “sink particle”
The particle is a solar system and its dynamics are modeled using another model
These particles need to be coupled to mesh cells
Validation
Different simulations disagree
Make prediction for problems with an analytic solution
Most codes pass these tests
Can compare simulations to observations
Mass spectrum of stars
Amount of hot gas in the galaxy